I often get questions from students about the best translation of some verse. Usually, the difference is between "literal" translation (such as ESV or NASB) and "dynamic" translation (such as the NIV or NLT). These two types are also called "formal" (because they try, when possible, to follow the forms and word order of the original Greek or Hebrew sentences) and "functional" (because they try to preserve the function or meaning of a whole sentence). Another way that these two types of translations are sometimes characterized is "word-for-word" and "thought-for-thought." A good book that clearly and succinctly explores these two translation philosophies is How to Choose a Translation For All Its Worth, by Gordon Fee and Mark Strauss.
A recent question emailed to me about the translation of John 3:21 reveals the difference in approaches. The underlined phrase in each (below) is a translation of the underlined Greek verb.
Greek: ὁ δὲ ποιῶν τὴν ἀλήθειαν ἔρχεται πρὸς τὸ φῶς, ἵνα φανερωθῇ αὐτοῦ τὰ ἔργα ὅτι ἐν θεῷ ἐστιν εἰργασμένα.
My formal translation: But the one who does the truth comes to the light, so that his works may be revealed that they are worked in God.
ESV: But whoever does what is true comes to the light, so that it may be clearly seen that his works have been carried out in God.
NLT: But those who do what is right come to the light so others can see that they are doing what God wants.
There are several differences between the translations, but the most important one is who the works are revealed to. The ESV (and other formal translations, like the NASB) leaves it unclear, but the first impression of most readers is that the works are revealed to God. The NLT (and some other functional translations like the CEV) specifies that the works are revealed to other people.
Part of the change that the NLT makes is converting the Greek passive "may be seen" into an active "so that [others] can see." It is common for functional translations to convert passive verbs to active for greater clarity. Nothing wrong with that - formal translations sometimes do the same to make more sense in English (Matt 5:7, for example). In this verse, converting the passive "may be seen" to an active verb requires specifying who it is revealed to. Should it be translated "so that God can see" or "so that others can see"? If the sentence was ambiguous in Greek, it would be best to leave it ambiguous in English, or maybe pick the most likely one and put the other choice in a footnote.
However, it turns out that this verse was not ambiguous to a native Greek speaker. The Greek verb for reveal in this verse is phaneroo (φανερόω). Elsewhere in John, and in general throughout the NT, phaneroo refers to revelation to humans, not to God (John 2:11, 7:4, 9:3, 17:6, 21:1). Knowing this, the translators of the NLT decided to make it clear in the translation that the the works are revealed to other people.
While there are good reasons to have "literal" translations like the ESV, it is interesting that in this case, the NLT more clearly communicates the meaning of the sentence by being less "literal."